Question: Simplify the following expression: $ n = \dfrac{9}{4} + \dfrac{5r + 7}{-5r} $
Solution: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{-5r}{-5r}$ $ \dfrac{9}{4} \times \dfrac{-5r}{-5r} = \dfrac{-45r}{-20r} $ Multiply the second expression by $\dfrac{4}{4}$ $ \dfrac{5r + 7}{-5r} \times \dfrac{4}{4} = \dfrac{20r + 28}{-20r} $ Therefore $ n = \dfrac{-45r}{-20r} + \dfrac{20r + 28}{-20r} $ Now the expressions have the same denominator we can simply add the numerators: $n = \dfrac{-45r + 20r + 28}{-20r} $ $n = \dfrac{-25r + 28}{-20r}$ Simplify the expression by dividing the numerator and denominator by -1: $n = \dfrac{25r - 28}{20r}$